Details

analyze259.0ms (8.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample38.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	140×	body	160	valid
8.0ms	283×	pre	80	true
5.0ms	116×	body	80	valid
1.0ms	27×	body	80	nan

simplify186.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune10.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.5b

Counts

2 → 2

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
27.4b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 72

Calls

4 calls:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))

series53.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
3.0ms	(* (* 3.0 a) c)

simplify43.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	6060	1115

prune160.0ms (5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	79	7	86

Merged error: 0.5b

Counts

86 → 7

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.3b	(* 3.0 (* a c))
0.3b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
0.4b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite45.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
28×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`pow1` `associate-/l*`
12×	`add-cube-cbrt`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
6×	`associate-l` `pow-prod-down` `associate-/r/`
4×	`distribute-rgt-neg-in` `sqrt-prod` `div-inv` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 123

Calls

4 calls:

16.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a c))
4.0ms	(* 3.0 (* a c))

series104.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
42.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
3.0ms	(* 3.0 (* a c))
3.0ms	(* 3.0 (* a c))

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5025	2216

prune279.0ms (8.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	5	0	5
Picked	1	0	1
Done	1	0	1
Total	135	7	142

Merged error: 0b

Counts

142 → 7

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.2b	(/ (* (/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) a) a)
0.2b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
0.3b	(* 3.0 (* a c))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`pow1`
7×	`add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp`
3×	`times-frac` `diff-log` `associate-l` `pow-prod-down` `associate-/r*`
2×	`sub-neg` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `frac-2neg` `associate-r` `neg-log` `associate-l/` `clear-num` `sqrt-prod` `-commutative` `div-inv` `associate-/l/` `associate-/l*`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/ (* (/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) a) a)
8.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))

series74.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (* (/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) a) a)
15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))

simplify42.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4993	1067
1	4993	1067

prune159.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 0b

Counts

89 → 6

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(- (neg b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))))
0.3b	(* a (* c (cbrt 3.0)))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0))))
0.3b	(* c (cbrt 3.0))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1` `add-exp-log`
22×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-cube-cbrt` `associate-r` `add-log-exp`
7×	`associate-l`
4×	`cbrt-prod`
3×	`*-commutative`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `distribute-rgt-neg-in` `neg-log` `sqrt-prod` `flip--`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0))))
11.0ms	(- (neg b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))))
5.0ms	(* a (* c (cbrt 3.0)))
5.0ms	(* c (cbrt 3.0))

series38.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (neg b) (sqrt (- (* b b) (* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0)))))))
8.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* a (* c (cbrt 3.0))))
5.0ms	(* a (* c (cbrt 3.0)))
5.0ms	(* c (cbrt 3.0))

simplify49.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4966	801
1	4966	801

prune195.0ms (6.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 0b

Counts

103 → 6

regimes172.0ms (5.3%)

Accuracy

Total 0.3b remaining (84.7%)

Threshold costs 0.3b (84.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	26
1	103	26

end0.0ms (0%)

sample1.1s (34%)

Algorithm

1×

intervals

Results

417.0ms	4461×	body	160	valid
255.0ms	9009×	pre	80	true
171.0ms	3539×	body	80	valid
50.0ms	1009×	body	80	nan

Details

analyze259.0ms (8.1%)

sample38.0ms (1.2%)

simplify186.0ms (5.8%)

prune10.0ms (0.3%)

localize11.0ms (0.3%)

rewrite31.0ms (1%)

series53.0ms (1.7%)

simplify43.0ms (1.4%)

prune160.0ms (5%)

localize13.0ms (0.4%)

rewrite45.0ms (1.4%)

series104.0ms (3.2%)

simplify55.0ms (1.7%)

prune279.0ms (8.7%)

localize15.0ms (0.5%)

rewrite33.0ms (1%)

series74.0ms (2.3%)

simplify42.0ms (1.3%)

prune159.0ms (5%)

localize17.0ms (0.5%)

rewrite35.0ms (1.1%)

series38.0ms (1.2%)

simplify49.0ms (1.5%)

prune195.0ms (6.1%)

regimes172.0ms (5.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (34%)

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